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Probability question

2013 · Shift 1 · Q38

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PYQ Library
JEE Advanced
Mathematics
Probability
2013 · Shift 1 · Q38

Probability question

2013 · Shift 1 · Q38

JEE AdvancedMathematicsProbabilityNumerical+4 / −1

Of the three independent events

{E_1},{E_2}

and

{E_3},

the probability that only

{E_1}

occurs is

\alpha ,

only

{E_2}

occurs is

\beta

and only

{E_3}

occurs is

\gamma .

Let the probability

p

that none of events

{E_1},{E_2}

or

{E_3}

occurs satisfy the equations

\left( {\alpha -2\beta } \right)p = \alpha \beta

and

\left( {\beta - 3\gamma } \right)p = 2\beta \gamma .

All the given probabilities are assumed to lie in the interval

(0, 1)

. Then

{{\Pr obability\,\,of\,\,occurrence\,\,of\,\,{E_1}} \over {\Pr obability\,\,of\,\,occurrence\,\,of\,\,{E_3}}}

Numerical answer

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